Comparison of experimental and finite element structure-borne flexural power measurements for a straight beam

Experimental and finite element methods are used to measure flexural powers in a straight beam model. The experimental methods use wave decomposition theory to obtain expressions for the incident, reflected and near-field wave spectra for a beam vibrating in flexure in terms of the measured auto- and cross-spectra of an array of closely spaced accelerometers. With expressions for the wave spectra, it is possible to measure the structural power and termination impedances related to the bending waves in the beam. The finite element approach models beams numerically by discretizing structures into elements which model elastic wave motions. The structural response is predicted for given loading and boundary conditions, and the power variables are calculated from element forces and velocities. The input forcing functions and end impedances (boundary conditions) of two experimental cases were applied to a finite element model. In one case, the beam was attached to a lightly damped mount and in the other case a heavily damped mount was used. Measured and predicted flexural powers were compared and showed mixed agreement. The directionality of power was accurately predicted, as was the general character of the power spectra. However, differences in power magnitudes, particularly in the lightly damped mounting case, were discovered. The power magnitude errors were attributed to accuracy limitations in the applied termination impedances. The results suggest that the finite element method may be used to predict accurately the direction and spectral trends of beam flexural power, but that numerical power magnitudes are highly dependent on accurate boundary condition quantification.